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Simplifying 49t2 + 100t + 20 = 0 Reorder the terms: 20 + 100t + 49t2 = 0 Solving 20 + 100t + 49t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.4081632653 + 2.040816327t + t2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + 2.040816327t + -0.4081632653 + t2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + 2.040816327t + t2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + 2.040816327t + t2 = 0 + -0.4081632653 2.040816327t + t2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 2.040816327t + t2 = -0.4081632653 The t term is 2.040816327t. Take half its coefficient (1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. 2.040816327t + 1.041232821 + t2 = -0.4081632653 + 1.041232821 Reorder the terms: 1.041232821 + 2.040816327t + t2 = -0.4081632653 + 1.041232821 Combine like terms: -0.4081632653 + 1.041232821 = 0.6330695557 1.041232821 + 2.040816327t + t2 = 0.6330695557 Factor a perfect square on the left side: (t + 1.020408164)(t + 1.020408164) = 0.6330695557 Calculate the square root of the right side: 0.795656682 Break this problem into two subproblems by setting (t + 1.020408164) equal to 0.795656682 and -0.795656682.Subproblem 1
t + 1.020408164 = 0.795656682 Simplifying t + 1.020408164 = 0.795656682 Reorder the terms: 1.020408164 + t = 0.795656682 Solving 1.020408164 + t = 0.795656682 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.020408164' to each side of the equation. 1.020408164 + -1.020408164 + t = 0.795656682 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + t = 0.795656682 + -1.020408164 t = 0.795656682 + -1.020408164 Combine like terms: 0.795656682 + -1.020408164 = -0.224751482 t = -0.224751482 Simplifying t = -0.224751482Subproblem 2
t + 1.020408164 = -0.795656682 Simplifying t + 1.020408164 = -0.795656682 Reorder the terms: 1.020408164 + t = -0.795656682 Solving 1.020408164 + t = -0.795656682 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.020408164' to each side of the equation. 1.020408164 + -1.020408164 + t = -0.795656682 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + t = -0.795656682 + -1.020408164 t = -0.795656682 + -1.020408164 Combine like terms: -0.795656682 + -1.020408164 = -1.816064846 t = -1.816064846 Simplifying t = -1.816064846Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.224751482, -1.816064846}
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